Finite Group DatabasebetaFinite Group Databasebeta| order | 10800 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×3−1+2⋊AGL(1,𝔽5) |
| Fitting, Hall | C52×3−1+2 ⋊ C42 |
| derived | C52×C9 ⋊ C3×C42 |
| Sylow | 3−1+2 ⋊ AGL(1,𝔽5)2 |
| Sylow | C52 ⋊ C4×3−1+2⋊C4 |
412 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
155 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)2×AGL(1,ℤ/9) |
| maximal normal subgroup of | AGL(1,𝔽5)2×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.